Special Matrices of Mathematical Physics: Stochastic, Circulant, and Bell Matrices

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World Scientific, 2001 - 340 páginas
This book expounds three special kinds of matrices that are of physical interest, centering on physical examples. Stochastic matrices describe dynamical systems of many different types, involving (or not) phenomena like transience, dissipation, ergodicity, nonequilibrium, and hypersensitivity to initial conditions. The main characteristic is growth by agglomeration, as in glass formation. Circulants are the building blocks of elementary Fourier analysis and provide a natural gateway to quantum mechanics and noncommutative geometry. Bell polynomials offer closed expressions for many formulas concerning Lie algebra invariants, differential geometry and real gases, and their matrices are instrumental in the study of chaotic mappings. Contents: Basics: Some Fundamental Notions; Stochastic Matrices: Evolving Systems; Markov Chains; Glass Transition; The Kerner Model; Formal Developments; Equilibrium, Dissipation and Ergodicity; Circulant Matrices: Prelude; Definition and Main Properties; Discrete Quantum Mechanics; Quantum Symplectic Structure; Bell Matrices: An Organizing Tool; Bell Polynomials; Determinants and Traces; Projectors and Iterates; Gases: Real and Ideal. Readership: Mathematical physicists, statistical physicists and researchers in the field of combinatorics and graph theory.
 

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Contenido

Some fundamental notions
3
Evolving systems
21
Glass transition
31
Formal developments
45
Equilibrium dissipation and ergodicity
63
Prelude
81
Discrete quantum mechanics
99
Quantum symplectic structure
127
Determinants and traces
183
Projectors and iterates
207
real and ideal
227
Appendix A Formulary
283
Circulant matrices
289
Bell matrices
302
Index
315
Derechos de autor

An organizing tool
149

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